6533b839fe1ef96bd12a66a3
RESEARCH PRODUCT
Controlled polyhedral sweeping processes: existence, stability, and optimality conditions
René HenrionAbderrahim JouraniBoris S. Mordukhovichsubject
49M25Applied Mathematics[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Existence of feasible solutions510Sweeping processQualitative stabilityOptimal controlMoving polyhedraOptimization and Control (math.OC)necessary optimality and suboptimality conditionsDiscrete approximationsFOS: MathematicsNecessary optimality and suboptimality conditions 2010 MSC: 49J5249J52 49J53 49K24 49M25[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]49K2449J52Mathematics - Optimization and ControlAnalysis49J53description
This paper is mainly devoted to the study of controlled sweeping processes with polyhedral moving sets in Hilbert spaces. Based on a detailed analysis of truncated Hausdorff distances between moving polyhedra, we derive new existence and uniqueness theorems for sweeping trajectories corresponding to various classes of control functions acting in moving sets. Then we establish quantitative stability results, which provide efficient estimates on the sweeping trajectory dependence on controls and initial values. Our final topic, accomplished in finite-dimensional state spaces, is deriving new necessary optimality and suboptimality conditions for sweeping control systems with endpoint constrains by using constructive discrete approximations.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2021-11-25 |